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\title{Optimizing Pedestrian Environments with Evolutionary Strategies}
\authorone{Marijn Swenne}
\authortwo{Thomas B\"ack}
%\authorthree{}
\affiliation{Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands}
\emailone{mswenne@liacs.nl}
\emailtwo{baeck@liacs.nl}
%\emailthree{}

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\begin{document}
\vspace{2cm}
\maketitle
\vspace{-3cm}

\large
\bigskip
\bigskip
\bigskip
\begin{multicols}{3}


%\vspace{1cm}
%\noindent
%Here, we will focus on projections
%obtained by parallel beams through a finite object.

%\begin{equation}\label{eq:radon_line}
%R_f\left(L\right) = \int_L \! f\left(\ell\right) \, d\ell.
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%\begin{figure}[t]
%\begin{subfigure}[b]{0.49\textwidth}
%  \centering
%  \includegraphics[width=0.9\textwidth]{goffman_hor}
%  \caption{(a) Goffman Scanning}
%  \label{fig:scanning}
%\end{subfigure}
%\begin{subfigure}[b]{0.49\textwidth}
%  \centering
%  \includegraphics[width=0.9\textwidth]{goffman_hor}
%  \caption{(b) Agent speed (circle) and average speed on edge (rectangle) }
%  \label{fig:congestion_information}
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%\caption{Agent perception in the social forces model and path selection.}
%\end{figure}






\section*{\textcolor{edlogoblue}{Pedestrian Simulator}}
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
\vspace{5mm}
The simulator developed for this research is based on the \textcolor{liacsred}{Social Forces Model}.
\vspace{5mm}
\end{minipage}}

\bigskip
\noindent
The Social Forces Model describes the movement of pedestrians as a results of a summation of social forces being: obstacle repulsion and goal attraction. 

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.2\textwidth]{goffman_hor.pdf}
  \label{fig:scanning}
\end{figurehere}
\end{center}

\bigskip
\noindent
Our selection process that determines which obstacles repel a pedestrian is based on research by Goffman on pedestrian perception. He observed pedestrians and developed a model describing how pedestrians take note of their fellow pedestrians called \textcolor{liacsred}{scanning}. In this model a pedestrians influence is determined by its proximity, its radial orientation and whether they are separated by other pedestrians.

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.2\textwidth]{sc_paths.pdf}
  \label{fig:sc_paths}
\end{figurehere}
\end{center}

\bigskip
\noindent
To determine the goal attraction, a path $P$ from the agents current position to it's goal is created with use of a \textcolor{liacsred}{Reduced Visibility Graph} $G$. The Reduced Visibility Graph is constructed from the borders around static obstacles that are obtained when tracing around them while keeping a distance equal to the agents radius.

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.2\textwidth]{sc_attractorpoint.pdf}
  \label{fig:attractorpoint}
\end{figurehere}
\end{center}

\bigskip
\noindent
On this path $P$ an \textcolor{liacsred}{attractor point} $ap$ is selected that is used to determine the direction of the \textcolor{liacsred}{goal attraction}. We do this by creating an attractor region $R$ around the agent and selecting the attractor point $ap$ where the the border of $R$ cuts $P$ or the last point on $P$ if no such point exists.

\bigskip
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
\vspace{5mm}
When calculating a route, it is the \textcolor{liacsred}{expected travel time} that determines the most desirable path.
\vspace{5mm}
\end{minipage}}

\bigskip
\noindent
When agents select their path, \textcolor{liacsred}{congestion} is taken into account. Every edge of $P$ contains congestion data, being the average speed of agents that walk over that edge. An agent is considered to be walking over an edge if the circle representing the agent overlaps with the edge. 

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.2\textwidth]{congestion.pdf}
  \label{fig:congestion}
\end{figurehere}
\end{center}

\bigskip
\noindent
Shown above is an example where the circles represent the agents which their walking speed and the rectangular box representing the edge information.

\section*{\textcolor{edlogoblue}{Evolutionary Strategy}}
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
\vspace{5mm}
An \textcolor{liacsred}{Evolutionary Strategy} (ES) optimizes multidimensional real valued problems.
\vspace{5mm}
\end{minipage}}

\bigskip
\noindent
It is a metaheuristic optimization algorithm belongs to a group called Evolutionary Algorithms (EA). An EA optimizes with use of mechanics inspired by biological evolution being: reproduction, mutation, recombination and selection. 

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.3\textwidth]{ES_expl.pdf}
  \label{fig:ES_expl}
\end{figurehere}
\end{center}

\bigskip
\noindent
We use a  $(1 , \lambda)$-ES with $\lambda = 10$. To try and find the best solution with this particular ES, an initial collection of 10 solutions is created after which the fitness of each member is determined. Now a cycle or generation is repeated until a stopping criteria is satisfied (in our case, 90 generations). In this cycle, the best parents is selected on fitness. From those parent 10 new solutions or children are created with use of mutation. These children form the new population which is then evaluated completing the cycle.

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\section*{\textcolor{edlogoblue}{Experiment}}
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
\vspace{5mm}
The \textcolor{liacsred}{Evolutionary Strategy} optimizes the position and size of pillars in a corridor by using the \textcolor{liacsred}{pedestrian simulator} to measure fitness.
\vspace{5mm}
\end{minipage}}

\bigskip
\noindent
In our corridor experiment we have two groups of agents starting at opposite sides of a corridor with each group wanting to reach the opposite side. The 5 obstacles represent pillars that should be arranged as to maximise agents efficiency which means minimizing the average time between agents being spawned and removed.

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.2\textwidth]{corridorsetup.pdf}
  \label{fig:corridorsetup}
\end{figurehere}
\end{center}


\section*{\textcolor{edlogoblue}{Results}}
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
\vspace{5mm}
\textcolor{liacsred}{Emergent behaviour} is observed, implying the simulator reproduces pedestrian behaviour.
\vspace{5mm}
\end{minipage}}

\bigskip
\noindent
Three runs were executed for the corridor experiment. In the following example the evolution of the population fitness and stepsize is shown over the course of one run.

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.3\textwidth]{str_evo_ES2.pdf}
  \label{fig:str_evo_ES2}
\end{figurehere}
\end{center}

\bigskip
\noindent
From each run, the best solution was selected and labeled C1, C2 and C3. We then compare the pedestrian efficiency for these 3 solutions with the 3 expert solutions for different pedestrian densities or spawn frequencies. 

\bigskip
\colorbox{someblue}{
\begin{minipage}[c]{23cm}
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Optimization can clearly \textcolor{liacsred}{increase efficiency} in the corridor environment with high density.
\vspace{5mm}
\end{minipage}}


\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.3\textwidth]{str_fitcomp.pdf}
  \label{fig:str_fitcomp}
\end{figurehere}
\end{center}

\bigskip
\noindent
In the visual representation of the three expert environments (left) and the three found by the ES (right) the configuration of agents is shown after 20 seconds.

\bigskip
\begin{center}
\begin{figurehere}
  \includegraphics[width=0.15\textwidth]{str_Empty_2.png}
  \includegraphics[width=0.15\textwidth]{str_ESC1_2.png}
  \includegraphics[width=0.15\textwidth]{str_Middle23_2.png}
  \includegraphics[width=0.15\textwidth]{str_ESC2_2.png}
  \includegraphics[width=0.15\textwidth]{str_Middlecentre_2.png}
  \includegraphics[width=0.15\textwidth]{str_ESC3_2.png}
  \label{fig:str}
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\end{center}

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\section*{\textcolor{edlogoblue}{Conclusions:}}
\begin{itemize}
\item Pedestrian simulator shows emergent behaviour;
\item Pedestrian simulator usable as fitness function;
\item Adding obstacles to corridor can increase pedestrian efficiency.
\end{itemize}
\section*{\textcolor{edlogoblue}{Future Research:}}
\begin{itemize}
\item Psycological agent model;
\item Injury measurement;
\end{itemize}

\end{multicols}

\end{document}
